Problem: Solve for $x$ and $y$ using elimination. ${-6x-y = -44}$ ${-5x+y = -33}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-11x = -77$ $\dfrac{-11x}{{-11}} = \dfrac{-77}{{-11}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-6x-y = -44}\thinspace$ to find $y$ ${-6}{(7)}{ - y = -44}$ $-42-y = -44$ $-42{+42} - y = -44{+42}$ $-y = -2$ $\dfrac{-y}{{-1}} = \dfrac{-2}{{-1}}$ ${y = 2}$ You can also plug ${x = 7}$ into $\thinspace {-5x+y = -33}\thinspace$ and get the same answer for $y$ : ${-5}{(7)}{ + y = -33}$ ${y = 2}$